Algebra Examples

$3.4 > x + \frac{2}{3}$

Step 1

Rewrite so $x$ is on the left side of the inequality.

$x + \frac{2}{3} < 3.4$

Step 2

Move all terms not containing $x$ to the right side of the inequality.

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Step 2.1

Subtract $\frac{2}{3}$ from both sides of the inequality.

$x < 3.4 - \frac{2}{3}$

Step 2.2

To write $3.4$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$x < 3.4 \cdot \frac{3}{3} - \frac{2}{3}$

Step 2.3

Combine $3.4$ and $\frac{3}{3}$ .

$x < \frac{3.4 \cdot 3}{3} - \frac{2}{3}$

Step 2.4

Combine the numerators over the common denominator.

$x < \frac{3.4 \cdot 3 - 2}{3}$

Step 2.5

Simplify the numerator.

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Step 2.5.1

Multiply $3.4$ by $3$ .

$x < \frac{10.2 - 2}{3}$

Step 2.5.2

Subtract $2$ from $10.2$ .

$x < \frac{8.2}{3}$

Step 2.6

Divide $8.2$ by $3$ .

$x < 2.7\overline{3}$

Step 3

The result can be shown in multiple forms.

Inequality Form:

$x < 2.7\overline{3}$

Interval Notation:

$(- \infty, 2.7\overline{3})$